You can put this solution on YOUR website! -3n < 81
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You need to solve this inequality for +n. You can operate on the inequality just as you would
an equation ... with a single exception ... that exception is that if you multiply or divide
both sides of the inequality by a negative number you have to also reverse the direction of
the inequality sign.
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This being the case, you can solve the given inequality by dividing both sides by -3, the
multiplier of the n term. When you divide both sides by -3 (and reversing the direction
of the inequality sign because you are dividing by a negative number), the resulting
inequality is:
.
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and the right side simplifies to:
.
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That means that the original inequality will be true as long as n is greater than -27.
That means that if n is a value to the right of -27 on the number line, the inequality
will be true. Let's try a couple of values just to help convince ourselves that our answer
is correct. For example, what happens if n is -28 ... put -28 in for n in the original
inequality ... and it becomes:
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(-3)*(-28) < 81
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Multiply out the left side and you get:
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+ 84 < 81
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This obviously is not true ... and that should be no surprise because we had found that
n had to be greater than -27 to work. So let's try n = -26 ... that's a value of n
that is greater than -27 and so it should work. Substitute - 26 for n in the original
inequality and you get:
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(-3)*(-26) < 81
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Multiply out the left side and you get:
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+78 < 81
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That is true ... 78 is less than 81. Therefore, we have a couple of examples that help
to confirm that if n is greater than -27 it works, but if n is less than -27 it does not
work.
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It never hurts to check a few values to confirm your answer.
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Hope this shows you that you can work inequalities as you would an equation ... except
for dividing and multiplying by negative numbers.
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